The Yang-Baxter equation, that comes from the papers due by Yang  and Baxter [1]}, is a basic equation of statistical mechanics. Classifying the solutions of the Yang-Baxter equation seems to be hard and it is still an open problem. In 1992 Drinfel'd [2]} moved the interest of several researchers for finding and classifying a particular class of solutions of this equation, the so-called set-theoretic solutions. Namely, a set-theoretic solution of the Yang-Baxter equation, or simply a solution, on a non-empty set \(X\)  is a pair \(\left(X,r\right)\) , where
\(r:X\times X\rightarrow X\times X\)  is a map such that the relation
\(\left(r\times \operatorname{id}_X\right)\left(\operatorname{id}_X\times r\right)\left(r\times \operatorname{id}_X\right)=\left(\operatorname{id}_X\times r\right)\left(r\times \operatorname{id}_X\right)\left(\operatorname{id}_X\times r\right)\) 
